Yes, a little bit, but not enough to bother me. I don't press too long though. Just long enough to set the seam. It sure rips off easily though! Actually, I found that it doesn't curl much more than the computer paper did.
I also got a huge roll of "examine table" paper from my chiropractor (who is also a quilting friend LOL) because they'd sent her the wrong kind and it's thin like the tracing paper and I've used it too! Works like a charm. Only problem is (and I'm going to admit how lazy I can be now LOL!!) I have to cut it into paper size sheets to get it in the printer. Golden Threads quilting paper works too, but like the other, it's too wide so it has to be cut to fit my printer. Works in a pinch though! :)